Trigo dilemma

Geometry Level 4

(sec210+tan10)(sec250tan50)(sec270+tan70) \left(\sec^{2}10^{\circ}+\tan 10^{\circ}\right)\left(\sec^{2} 50^{\circ} - \tan 50^{\circ}\right)\left(\sec^{2} 70^{\circ}+\tan 70^{\circ}\right)

The value of the expression above can be represented in the form abb\dfrac{a-\sqrt{b}}{b} where aa and bb are positive coprime integers. Find the value of a+b2a+b^2.

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